Equations of uniformly accelerated motion
3 marks · NormalA football is kicked along a flat field so it travels in a straight line from rest and comes to a stop again. Its initial velocity is 0 m/s; it accelerates uniformly to reach 12 m/s, moves at that speed for a while, then slows uniformly to rest. The acceleration and deceleration are both 4 m/s².
Calculate the time it takes for the football to accelerate from rest up to its top speed.
How far does the football travel while accelerating to top speed?
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 3 s · must show Uses a = (v-u)/t or rearranged form with values
(b) 18 m · must show Uses v^2 = u^2 + 2as and rearranges for s
Common mistakes: Mixing up acceleration and deceleration; Using wrong equation for s
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Applies a = (v-u)/t or v = u + at correctly.
A1 (a) · 1 mark · Obtains t = 3 s (allow 2.9–3.1 s) (follow-through)
M2 (b) · 1 mark · Substitutes into v^2 = u^2 + 2as or s = 0.5 a t^2 using correct values for part b. (follow-through)
Worked solution
a) Use v = u + at; here u = 0, v = 12, a = 4: 12 = 0 + 4t t = 12 / 4 = 3 s
b) Use v^2 = u^2 + 2as: 12^2 = 0 + 2 × 4 × s 144 = 8s s = 18 m