A car is moving on circular track of radius 150 m and at some time its speed is decreasing at a rate of 8 m / s 2, if the speed of car at that instant was 30 m / s, net acceleration of the car will be

Question

A car is moving on circular track of radius 150 m and at some time its speed is decreasing at a rate of 8 m / s 2, if the speed of car at that instant was 30 m / s, net acceleration of the car will be (A) 8 m / s 2 (B) 6 m / s 2 (C) 10 m / s 2 (D) 14 m / s 2

Tardigrade Admin · Accepted Answer

ac=(v2/r)=(30 × 30/150)=6 m / s 2 at=8 m / s 2 both accelerations are always perpendicular a=√ac2+at2=√(6)2+(8)2 =10 m / s 2

Q. A car is moving on circular track of radius $150 m$ and at some time its speed is decreasing at a rate of $8 m / s^{2}$ , if the speed of car at that instant was $30 m / s$ , net acceleration of the car will be

$8 m / s^{2}$

$6 m / s^{2}$

$10 m / s^{2}$

$14 m / s^{2}$

$a_{c} = \frac{v ^{2}}{r} = \frac{30 \times 30}{150} = 6 m / s^{2}$
$a_{t} = 8 m / s^{2}$
both accelerations are always perpendicular
$a = a_{c}^{2} + a_{t}^{2} = (6)^{2} + (8)^{2}$
$= 10 m / s^{2}$

Q. A car is moving on circular track of radius 150m and at some time its speed is decreasing at a rate of 8m/s2, if the speed of car at that instant was 30m/s, net acceleration of the car will be

8m/s2

6m/s2

10m/s2

14m/s2