Question

A car accelerates from rest at a constant rate a for some time after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t, the maximum velocity acquired by the car is given by

• A. $\left( \frac{\alpha^{2} + \beta^{2}}{\alpha\beta} \right)t$
• B. $\left( \frac{\alpha^{2} - \beta^{2}}{\alpha\beta} \right)t$
• C. $\left( \frac{\alpha + \beta}{\alpha\beta} \right)t$
• D. $\left( \frac{\alpha\beta}{\alpha + \beta} \right)t$

Answer 1

Answer: (D)

$\left( \frac{\alpha\beta}{\alpha + \beta} \right)t$

Answer 2

Using, v = u + at₁, we get,

t₁ = $\frac{v}{\alpha}$ ( u = 0)

for retarded motion,

0 = v - β/2 or t₂ = v/β

Total time t = t₁ + t₂ = $\frac{v}{\alpha} + \frac{v}{\beta}$

= v$\left( \frac{\alpha + \beta}{\alpha\beta} \right)$or u = $\left( \frac{\alpha\beta}{\alpha + \beta} \right)$t