SUVAT single equation: straightforward find

7 A walker travels along a straight road passing through the points \(A\) and \(B\) on the road with speeds \(0.9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(1.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. The walker's acceleration between \(A\) and \(B\) is constant and equal to \(0.004 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Find the time taken by the walker to travel from \(A\) to \(B\), and find the distance \(A B\). A cyclist leaves \(A\) at the same instant as the walker. She starts from rest and travels along the straight road, passing through \(B\) at the same instant as the walker. At time \(t \mathrm {~s}\) after leaving \(A\) the cyclist's speed is \(k t ^ { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(k\) is a constant.
2. Show that when \(t = 64.05\) the speed of the walker and the speed of the cyclist are the same, correct to 3 significant figures.
3. Find the cyclist's acceleration at the instant she passes through \(B\).

1. A car is initially at rest on a straight horizontal road.

The car then accelerates along the road with a constant acceleration of \(3.2 \mathrm {~ms} ^ { - 2 }\) Find

1. the speed of the car after 5 s ,
2. the distance travelled by the car in the first 5 s .

5 A car of mass 1200 kg travels from rest along a straight horizontal road. The driving force is 4000 N and the total of all resistances to motion is 800 N .
Calculate the velocity of the car after 9 seconds.

9 In an experiment, a small box is hit across a floor. After it has been hit, the box slides without rotation. The box passes a point A. The distance the box travels after passing A before coming to rest is \(S\) metres and the time this takes is \(T\) seconds. The only resistance to the box's motion is friction due to the floor. The mass of the box is \(m \mathrm {~kg}\) and the frictional force is a constant \(F\).

1. 1. Find the equation of motion for the box while it is sliding.
   2. Show that \(S = k T ^ { 2 }\) where \(k = \frac { F } { 2 m }\).
2. Given that \(k = 1.4\), find the value of the coefficient of friction between the box and the floor.

1 A train travels along a straight horizontal track. It is travelling at a speed of \(12 \mathrm {~ms} ^ { - 1 }\) when it begins to accelerate uniformly. It reaches a speed of \(40 \mathrm {~ms} ^ { - 1 }\) after accelerating for 100 seconds.

1. 1. Show that the acceleration of the train is \(0.28 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
   2. Find the distance that the train travelled in the 100 seconds.
2. The mass of the train is 200 tonnes and a resistance force of 40000 N acts on the train. Find the magnitude of the driving force produced by the engine that acts on the train as it accelerates.

1 A crane is used to lift a crate, of mass 70 kg , vertically upwards. As the crate is lifted, it accelerates uniformly from rest, rising 8 metres in 5 seconds.

1. Show that the acceleration of the crate is \(0.64 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
2. The crate is attached to the crane by a single cable. Assume that there is no resistance to the motion of the crate. Find the tension in the cable.
3. Calculate the average speed of the crate during these 5 seconds.

1 A crane is used to lift a load, using a single vertical cable which is attached to the load. The load accelerates uniformly from rest. When it has risen 0.9 metres, its speed is \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. 1. Show that the acceleration of the load is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
   2. Find the time taken for the load to rise 0.9 metres.
2. Given that the mass of the load is 800 kg , find the tension in the cable while the load is accelerating.

3 A car is travelling at a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) along a straight horizontal road. The driver applies the brakes and a constant braking force acts on the car until it comes to rest.

1. Assume that no other horizontal forces act on the car.
   1. After the car has travelled 75 metres, its speed has reduced to \(10 \mathrm {~ms} ^ { - 1 }\). Find the acceleration of the car.
   2. Find the time taken for the speed of the car to reduce from \(20 \mathrm {~ms} ^ { - 1 }\) to zero.
   3. Given that the mass of the car is 1400 kg , find the magnitude of the constant braking force.
2. Given that a constant air resistance force of magnitude 200 N acts on the car during the motion, find the magnitude of the constant braking force.
   (1 mark)

1 A car is travelling along a straight horizontal road. It is moving at \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it starts to accelerate. It accelerates at \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 12 seconds.

1. Find the speed of the car at the end of the 12 seconds.
2. Find the distance travelled during the 12 seconds.
3. The mass of the car is 1400 kg . A horizontal forward driving force of 1600 N acts on the car during the 12 seconds. Find the magnitude of the resistance force that acts on the car.
   [0pt] [3 marks]
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13 A vehicle, of total mass 1200 kg , is travelling along a straight, horizontal road at a constant speed of \(13 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) This vehicle begins to accelerate at a constant rate.
After 40 metres it reaches a speed of \(17 \mathrm {~ms} ^ { - 1 }\) Find the resultant force acting on the vehicle during the period of acceleration.

12 A car is travelling along a straight horizontal road with initial velocity \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) The car begins to accelerate at a constant rate \(a \mathrm {~ms} ^ { - 2 }\) for 5 seconds, to reach a final velocity of \(4 u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Express \(a\) in terms of \(u\).
Circle your answer.
[0pt] [1 mark] \(a = 0.2 u\) \(a = 0.4 u\) \(a = 0.6 u\) \(a = 0.8 u\)