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Chapter 5: Q2. (page 130)

A car rounds a curve at a steady 50 km/h. If it rounds the same curve at a steady 70 km/h, will its acceleration be any different? Explain.

Short Answer

Expert verified

Yes, the acceleration will increase as the speed of the car increases.

Step by step solution

01

Step 1. Given Data

The initial speed of the car is v1=50km/h.

The final speed of the car is v2=70km/h.

02

Step 2. Understanding the centripetal acceleration

According to the relation of the centripetal acceleration, it is evident that centripetal acceleration gets affected by the change in speed of the vehicle and radius of the vehicle.

03

Step 3. Evaluating the variation in acceleration of the car

The relation of centripetal acceleration can be written as:

a=v2r

Here, v is the speed of the car and r is the radius.

The ratio of acceleration from the above relation is given by,

a2a1=v22rv12ra2a1=v22v12

On plugging the values in the above relation.

a2a1=70km/h250km/h2a2a1=1.96a2=1.96a1

Thus, the acceleration will increase due to the increase in speed of the car.

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