1) a car accelerates uniformly from rest and reaches a speed of 19.8 m/s in 7 s. the diameter of a tire is 38.5 cm. find the number of revolutions the tire makes during this motion, assuming no slipping. answer in units of rev.

2) a wheel has a radius of 4.8 m. how far (path length) does a point on thecircumference travel if the wheel is rotatedthrough an angle of 54◦? answer in units of m.

3) how far (path length) does a point on thecircumference travel if the wheel is rotatedthrough an angle of 319 rad? answer in units of m

1) 57 revolutions.

2) 4.52 m

3) 1531.2 m

Explanation:

Question 1:

Given:

Initial velocity,

Final velocity,

Time,

Acceleration,

Now, displacement of the tire is given as:

Displacement of tire in 1 revolution is equal to its circumference.

Therefore, displacement in 1 revolution =

Now, number of revolutions is given as:

Therefore, the number of revolutions are 57.

Question 2:

Given:

Radius of the wheel is,

Angle of rotation is, °

Converting degree to radians, we get:

Now, path length is given as:

Therefore, the path length of a point on the wheel is 4.52 m

Question 3:

Radius of the wheel is,

Angle of rotation is, radians

Now, path length is given as:

Therefore, the path length of a point on the wheel is 1531.2 m.