Question

A car is moving with a velocity of 80 km/h. Brakes are applied to bring the car to rest in 5 min. Find the acceleration.

Answer 1

Answer:

$\boxed{\sf Acceleration \ (a) = \frac{2}{27} \ m/s^2 }$

Given:

Initial velocity (u) = 80 km/h

= $\sf \frac{200}{9}$ m/s

Final velocity (v) = 0 km/h = 0 m/s

Time taken (t) = 5 min = 300 sec

To Find:

Acceleration (a)

Explanation:

$\sf Converting \ velocity \ from \ km/h \ to \ m/s : \\ \sf 1km/h \ = \frac{5}{18} \ m/s \\ \\ \\ \sf \implies 80km/h = \ 80 \times \frac{5}{18} \ m/s \\ \\ \sf = \frac{400}{18} \ m/s \\ \\ \sf = \frac{200}{9} \ m/s$

$\sf Converting \ time \ from \ min \ to \ sec: \\ \sf 1 \ min = 60 \ sec \\ \\ \sf \implies 5 \ min = 5 \times 60 sec \\ \sf = 300 \ sec$

$\sf From \ 1^{st} \ equation \ of \ motion: \\ \sf \implies v = u + at \\ \\ \sf \implies 0 = \frac{200}{9} + a(300) \\ \\ \sf \implies 300a + \frac{200}{9} = 0 \\ \\ \sf \implies 300a = - \frac{200}{9} \\ \\ \sf \implies a = - \frac{2 \cancel{00}}{9} \times \frac{1}{3 \cancel{00}} \\ \\ \sf \implies a = - \frac{2}{9 \times 3} \\ \\ \sf \implies a = \frac{2}{27} \: m/s^2$