Moderate -0.3 This is a straightforward calculus mechanics question requiring students to differentiate to find velocity, set v=0 to find when the particle is at rest, then substitute back into the displacement equation. It's slightly easier than average because it's a direct application of standard techniques with no conceptual challenges, though the algebra (solving a cubic equation that factors nicely) adds minor complexity beyond pure recall.
A particle moves in a straight line starting from rest. The displacement \(s\) m of the particle from a fixed point \(O\) on the line at time \(t\) s is given by
$$s = t^2 - \frac{15}{4}t^2 + 6.$$
Find the value of \(s\) when the particle is again at rest. [4]
Allow unsimplified, including indices (including a +c
is A0).
1 1
v0 t2(20t25)0t...
Answer
Marks
Guidance
8
DM1
Attempting to find t by equating v to 0 and attempt to
solve a linear equation for t (if correct t = 2.25).
Must be of the form t = … .
15
s [0.9375]
Answer
Marks
Guidance
16
A1
Condone 0.938 .
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 3:
3 | For an attempt at differentiation. | *M1 | Decrease power by 1 and a change in coefficient in at
s
least one term. v is M0.
t
5 3 45 1
(v) t2 t2
2 8 | A1 | Allow unsimplified, including indices (including a +c
is A0).
1 1
v0 t2(20t25)0t...
8 | DM1 | Attempting to find t by equating v to 0 and attempt to
solve a linear equation for t (if correct t = 2.25).
Must be of the form t = … .
15
s [0.9375]
16 | A1 | Condone 0.938 .
4
Question | Answer | Marks | Guidance
A particle moves in a straight line starting from rest. The displacement $s$ m of the particle from a fixed point $O$ on the line at time $t$ s is given by
$$s = t^2 - \frac{15}{4}t^2 + 6.$$
Find the value of $s$ when the particle is again at rest. [4]
\hfill \mbox{\textit{CAIE M1 2023 Q3 [4]}}