Moderate -0.5 This is a standard two-equation kinematics problem using s = ut + ½at². Students substitute given values to form simultaneous equations and solve algebraically. While it requires careful algebraic manipulation, it's a routine textbook exercise with no conceptual difficulty or novel insight required, making it slightly easier than average.
A car moves in a straight line with initial speed \(u\) m s\(^{-1}\) and constant acceleration \(a\) m s\(^{-2}\). The car takes 5 s to travel the first 80 m and it takes 8 s to travel the first 160 m. Find \(a\) and \(u\). [6]
using speeds as u (at t = 0), u + 5a (at t = 5), u + 8a (at t = 8)
and then apply s = ½ × (u + v) × t
Answer
Marks
Guidance
80 = 5u + ½ × a × 52 → 5u + 12.5a = 80
A1
One correct equation in a and u
160 = 8u + 0.5a × 82 → 8u + 32a = 160
A1
Second correct equation in a and u
M1
Attempt to solve a pair of valid simultaneous equations for a
or u
8
a =
Answer
Marks
Guidance
3
A1
Allow a = 2.67
28
u =
Answer
Marks
Guidance
3
A1
Allow u = 9.33
6
Answer
Marks
Guidance
Question
Answer
Marks
Question 2:
2 | Possible equations include:
t = 0 to t = 5 → 80 = 5u + 12.5a
t = 0 to t = 8 → 160 = 8u + 32a
t = 5 to t = 8 → 80 = 3(u + 5a) + 4.5a
i.e. 80 = 3 u + 19.5a | M1 | Use the equation
s = ut + ½at 2 to set up one equation in u and a
or
using speeds as u (at t = 0), u + 5a (at t = 5), u + 8a (at t = 8)
and then apply s = ½ × (u + v) × t
80 = 5u + ½ × a × 52 → 5u + 12.5a = 80 | A1 | One correct equation in a and u
160 = 8u + 0.5a × 82 → 8u + 32a = 160 | A1 | Second correct equation in a and u
M1 | Attempt to solve a pair of valid simultaneous equations for a
or u
8
a =
3 | A1 | Allow a = 2.67
28
u =
3 | A1 | Allow u = 9.33
6
Question | Answer | Marks | Guidance
A car moves in a straight line with initial speed $u$ m s$^{-1}$ and constant acceleration $a$ m s$^{-2}$. The car takes 5 s to travel the first 80 m and it takes 8 s to travel the first 160 m. Find $a$ and $u$. [6]
\hfill \mbox{\textit{CAIE M1 2019 Q2 [6]}}