Question

A car is moving at a speed of 40 m/s on a circular
track of radius 400 m. This speed is increasing at
the rate of 3 m/s2. The acceleration of car is
(1) 4 m/s2
12 7 m/s2
(3) 5 m/s2
(4) 3 m/s2

Answer 1

Answer:

The answer is 5m/s²

Answer 2

Answer:

A car is moving at a speed of 40 m/s on a circular  track of a radius of 400 m. This speed is increasing at  the rate of 3 m/s2. The acceleration of the car is $5\ m/s^{2}$

Explanation:

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

For an object in a uniform circular motion, the radial acceleration ($a_r$) of that object 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,

$r = 400\ m$

$v = 40\ m/s$

Radial acceleration of the car,

$a_r =\frac{40^{2} }{ 400}} = 4\ m/s^{2}$

Increased acceleration $a_i = 3\ m/s^{2}$

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

$a = \sqrt{4^{2}+3^{2} } = \sqrt{25} = 5\ m/s^{2}$

Thus the answer is option (3).