(a)[3]
Show that the particle's acceleration changes instantaneously at $t = 10$.
(b)[6]
Find the total distance travelled by $P$ over $0 \leq t \leq 20$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particle $P$ travels along a straight line. Its velocity $v\,\text{m s}^{-1}$ at time $t$ seconds is defined by $v = 0.5t$ for $0 \leq t \leq 10$, and by $v = 0.25t^2 - 8t + 60$ for $10 \leq t \leq 20$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Treat acceleration as the gradient, giving $a=\frac{dv}{dt}=0.5$ at the start.” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI