Question

A bus moving on a straight road with a speed of 35 m/s is brought to rest after 20cm Calculate
a acceleration of bus
B) Time taken by the bus to come to res​

Answer 1

Given :

Initial speed of bus = 35 m/s

Final velocity = zero (i.e., at rest)

Distance covered = 20cm = 0.2m

To Find :

Acceleration and time taken by the bus to come to rest.

Solution :

❖ Here speed of bus is slowing down at a constant rate it means acceleration of bus is constant therefore equation of kinematics can be applied to solve this question$.$

♦ Acceleration of the bus :

• Acceleration is defined as the rate of change of velocity.

➙ v² - u² = 2as

➙ 0² - 35² = 2a(0.2)

➙ -1225 = 0.4a

➙ a = -1225/0.4

➙ a = -3062.5m/s²

[Negative sign shows retardation.]

♦ Calculation of time :

➙ v = u + at

➙ 0 = 35 + (-3062.5)t

➙ t = -35/(-3062.5)

➙ t = 0.01s

Answer 2

Understanding the concept :

This question says that there is a bus moving on a straight road with a speed of 35 m/s and after 20 cm it come at rest. Hence, the final velocity be 0 because at that time the body is at rest and we already know that when an object is on rest then the velocity becomes 0 by itself. Now as we see that distance covered is given in cm and speed in m so let's covert cm into m and we know that 1 m = 100 cm and 1 cm = 1/100 m hence, 20 / 100 = 0.2 metres.

Given that :

Initial speed = 35 m/s

Final velocity = 0

Distance covered = 20 cm ( 0.2 m )

To find :

Acceleration of bus.

Time taken by the bus to come to rest.

Solution :

Acceleration of bus = - 3062.5 m/s²

Time taken by the bus to come to rest = 0.01 seconds.

Using concept :

Kinematic equations :

Newton's first law of motion

Newton's third law of motion.

Using formula :

Newton's first law of motion = v = u + at

Newton's third law of motion = v² - u² = 2as

Where –

v is final velocity

u is initial velocity

a is acceleration

t is time

s is displacement or distance

Full solution :

Finding acceleration of the bus

☞ v² - u² = 2as

☞ 0² - 35² = 2a(0.2)

☞ - 1225 = 0.4a

☞ a = - 1225 / 0.4

☞ a = - 3062.5 m/s²

Finding time taken by the bus to come to rest.

☞ v = u + at

☞ 0 = 35 + (-3062.5)t

☞ t = -35 / -3062.5

☞ t = 35 / 3062.5

☞ t = 0.01s