<p>An electric vehicle starts from rest and accelerates at a rate <em>a</em><sub

Question

<p>An electric vehicle starts from rest and accelerates at a rate <em>a</em>₁ in a straight line until it reaches a speed of <em>v</em>. The vehicle then slows at a constant rate <em>a</em>₂ until it stops. <strong>(a)</strong> How much time elapses from start to stop? <strong>(b)</strong> How far does the vehicle move from start to stop? Give your answers in terms of the given variables.</p>

Explanation / Answer

a)
v = u + at
the time, t1 for the acceleration = (v-0)/a1 = v/a1

the time, t2 for the decceleration = (0-v)/-a2 = v/a2

total time = v/a1 + v/a2 = [v(a1 + a2)] / (a1a2) seconds

b)

d = 1/2 ( Vf + Vi ) × t

the distance, d1 for the acceleration = 0.5 (v + 0) * v/a1 = v2 /(2a1)

the distance, d2 for the decceleration = 0.5 (0 + v) * v/a2 = v2 /(2a2)

total distance = v2 /(2a1) + v2 /(2a2) = v2(2a1 + 2a2) /(2a1)(2a2) = [2v2(a1 + a2)] /(4a1a2) = v2(a1 + a2) /(2a1a2)

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