Question

if a car moving with a speed of 60m/s on a circular track of radius 3.6km. its speed is increasing at the rate of 2m/s2. find the acceleration of the car.

A) 2m/s2
B)9.8m/s2
C)3.8m/s2
D)2.23m/s2​

Answer 1

Answer:

If a car moves with a speed of 60 m/s on a circular track of a radius of 3.6  km. Its speed is increasing at the rate of 2 m/s. The net acceleration of the car will be $2.23\ m/s^2$. Thus the answer is option D

Explanation:      

Acceleration (a) is the rate of change of velocity with respect to time.

The radial acceleration ($a_r$) of an object in a uniform circular motion is the acceleration along the radius, directed towards the center which is given by the formula,

$a_r = \frac{v^{2} }{r}$      

Where v is the velocity of the car and r is the radius of the circular path.

From the question,

$r = 3.6\ km = 3.6\times10^{3}\ m$

$v = 60\ m/s$

Radial acceleration of the car,

$a_r =\frac{60^{2} }{ 3.6\times10^{3}} = 1\ m/s^{2}$

Increased acceleration $a_i = 2\ m/s^{2}$

Net acceleration of the car $a=\sqrt{a_{r}^{2}+a_{i}^{2}}$

$a = \sqrt{1^{2}+2^{2} } = \sqrt{5} = 2.23\ m/s^{2}$

Thus the answer is option D.