Question

As you drive down the road at 13 m/s , you press on the gas pedal and speed up with a uniform acceleration of 1.02 m/s2 for 0.70 s. If the tires on your car have a radius of 33 cm, what is their angular displacement during this period of acceleration?

Answer 1

The angular displacement is
`\theta = 28.33 \ rad`

Step-by-step explanation:

From the question we are told that

The speed of the driver is
`v =13 \ m/ s`

The acceleration of the driver is
`a = 1.02 \ m/s^2`

The time taken is
`t = 0.70 \ s`

The radius of the tire is
`r = 33 cm = 0.33 \ m`

The distance covered by the car during this acceleration can be calculated using the equation of motion as follows

`s = v*t +(1)/(2) * a * t^2`

Now substituting values

`s = 13 * 0.70 +(1)/(2) * 1.02 * (0.700)^2`

`s = 9.35 \ m`

Now the angular displacement of the car with respect to the tire movement can be represented mathematically as

`\theta = (s)/(r)`

substituting values

`\theta = (9.35)/(0.33)`

`\theta = 28.33 \ rad`