Question

The speed of a car changes from $\frac{5}{18}$ m/s to $\frac{18}{5}$ km/h in 13 s. The magnitude of acceleration of the car is

• A. Zero
• B. $0.25m/s^2$
• C. $\frac{1}{13}m/s^2$
• D. $\frac{1}{18}m/s^2$

Answer 1

The correct option is D $\frac{1}{18}m/s^2$

Initial speed of the car, $u=\frac{5}{18}m/s$
Final speed of the car, $v=\frac{18}{5}km/h=\frac{18}{5}\times \frac{5}{18}=1m/s$ $[\because 1km/s=\frac{5}{18}m/s]$
Time in which the velocity of the car changes from u to v, t = 13s
Using first equation of motion, v = u + at
Acceleration, $a=\frac{v-u}{t}$
$\Rightarrow a=\frac{1-\frac{5}{18}}{13}$
$\Rightarrow a=\frac{13}{13\times 18}$
$\Rightarrow a=\frac{1}{18}m/s^2$
Hence, the correct answer is option (d).