Question

A car moving with speed 30 m/s on a circular path
of radius 500 m. Its speed is increasing at the rate
of 2m/s2. The acceleration of the car is :-

Answer 1

Answer:

2.7 m/s²

Explanation:

Speed of the car = 30 m/s

circular path of radius 500 m

Its speed is increasing at the rate of 2m/s2.

Acceleration = ?

=> Total acceleration is equal to the root of the squared sum of centripetal acceleration and tangential acceleration.

Thus,  centripetal acceleration, a_n = v²/ radius = 30²/500

Tangential acceleration, a_t = 2 m/s²

=> Total acceleration:

a_total = √ a_t² + a_n²

= √2² + (30²/500)²

= √2² + 1.8²

= √4 + 3.24

= √7.24

= 2.7 m/s²

Answer 2

Answer:

    2.7 m/s²

Explanation:

=> It is given that,

Speed of a car = 30m/s

Radius of circular track =  500m.

Its speed is increasing at the rate of 2m/s2.

Acceleration = ?

=> Total acceleration is equal to the root of the squared sum of centripetal acceleration and tangential acceleration.  

Thus,  centripetal acceleration, a_n = v²/ radius = 30²/500

Tangential acceleration, a_t = 2 m/s²

=> Total acceleration:

a_total = √ a_t² + a_n²

= √2² + (30²/500)²

= √2² + 1.8²

= √4 + 3.24

= √7.24

= 2.7 m/s²

Thus, the value of the acceleration of a car is 2.7 m/s².