Question

A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west and the total acceleration of the car is 2.5m/s2 53 degrees north of west. Find the radial and tagential components of the acceleration of the car at that moment. If the cars tangential acceleration is constant how long will it take for it to make one full circle from the point at which its velocity is 24m/s west?

Answer 1

Answer with Explanation:

We are given that

Velocity,v=24 m/s west

Acceleration,a=
`2.5m/s^2`

`\theta=53^(\circ)`(N of W)

Horizontal component of acceleration=Tangential acceleration

Tangential acceleration,
`a_x=acos\theta=2.5cos53=1.505 m/s^2`

Radial acceleration=Vertical acceleration=
`a_y=asin\theta`

`a_y=2.5sin53=1.998 m/s^2`

Radial acceleration,
`a_y=(v^2)/(R)`

`1.998=((24)^2)/(R)`

`R=((24)^2)/(1.998)`

`R=288.29 m`

Time,
`t=(2\pi R)/(velocity)`

`t=(2\pi(288.29))/(24)`

`t=75.47 s`