First slide

The 3 equation for uniform acc

Question

A car starting from rest accelerates at the rate f through a distance s, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 s, then

Moderate

A

$s = \frac{1}{4} {ft}^{2}$
B

$s = \frac{1}{72} {ft}^{2}$
C

$s = \frac{1}{6} {ft}^{2}$
D

s = f t

Solution

See figure
Given that s + s₁ + s₂ = 15 s ...(1)

For motion along OA, we have
$v^{2} = 2 fs (∵ u = 0 and v = v)$
For motion along AB, s₁ = v t …(2)
For motion along BC
$v^{2} = 2 (f / 2) s_{2} . . . . (3) (∵ u = v, v = 0 and a = - f / 2)$
Solving above equations, we have
$s = \frac{1}{72} {ft}^{2}$

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