Question

A person driving a car with a speed of 72 km/h observes a boy crossing the road at a distance of 100 m from the car. Driver applies the brakes and retards the car with a retardation of 5 m/s² and is just able to avoid this accident. The reaction time of driver​

Answer 1

Explanation:

INITIAL VELOCITY=72KM/H=72×5/18=20M/S

DISTANCE=100M

ACCELERATION =-5M/S^2(AS THE BODY WAS RETARDING)

FINAL VELOCITY =0 (BODY COMES AT REST)

THEREFORE,

A=V-U/T

T=V-U/A

T=0-20/-5

T=4S

SINCE,T=4S WHEN THE CAR HITS THE BOY ,SO TO AVOID ACCIDENT IT SHOULD BE BEFORE THAT TIME

THEREFORE,3S

OPTION C

Answer 2

Given :

• Initial velocity of the car = 72 km/h
• Final velocity of the car = 0 m/s
• Distance = 100 m
• Retardation of the car = 5 m/s²

To find :

• Reaction time of the driver

Solution :

Firstly, we shall convert the initial velocity of the car from km/h into m/s. For that multiply the value by 5/18.

⇒ Initial velocity = 72 × 5/18

⇒ Initial velocity = 4 × 5

⇒ Initial velocity = 20 m/s

Now, we will use the first equation of motion to calculate the reaction time of the driver.

First equation of motion :-

• v = u + at

where,

• v denotes the final velocity
• u denotes the initial velocity
• a denotes the acceleration
• t denotes the time

we have,

→ Initial velocity (u) = 20 m/s

→ Final velocity (v) = 0 m/s

→ Acceleration (a) = - 5 m/s² [Here we will take the sign of the acceleration as negative. Because in the question we are given the value of retardation and negative acceleration is known as retardation. So, if we convert retardation into acceleration the value will get negative sign.]

Substituting the given values :-

⇒ 0 = 20 + (- 5)(t)

⇒ 0 = 20 - 5t

⇒ - 20 = - 5t

⇒ 20 = 5t

⇒ 20/5 = t

⇒ 4 = t

Time = 4 seconds.

Now, we will calculate the distance travelled by the car in 4 seconds by using the second equation of motion.

• s = ut + ½ at²

where,

• s denotes the distance travelled
• u denotes the initial velocity
• a denotes the acceleration
• t denotes the time

Substituting the given values :

⇒ s = (20)(4) + ½ × (-5) × (4)²

⇒ s = 80 + ½ × (-5) × 16

⇒ s = 80 + (-5) × 8

⇒ s = 80 - 40

⇒ s = 40

The distance travelled = 40 m

⇒ The remaining distance = 100 - 40

⇒ The remaining distance = 60 m

Now, to calculate the time we will use the following formula,

• Time = Distance ÷ Speed

⇒ Time = 60/20

⇒ Time = 6/2

⇒ Time = 3

Therefore, the reaction time of the driver = 3 seconds