RaySix

Post

at November 3rd 2023, 7:29:05 pm.

Question:

A car is initially at rest and then accelerates uniformly at a rate of 3 m/s^2 for a distance of 100 meters.

a) Calculate the final velocity of the car.

b) How much time does it take for the car to reach this final velocity?

c) Determine the time it takes for the car to reach the midpoint of this distance.

Assume one-dimensional motion and neglect any external factors such as air resistance.

Answer:

a) To find the final velocity of the car, we can use the formula:

v = u + at

where v is the final velocity, u is the initial velocity (which is 0 m/s in this case), a is the acceleration, and t is the time.

Substituting the given values, we have:

v = 0 + (3 \, \text{m/s}^2) \cdot t

Since the initial velocity is zero, we can simplify this equation to:

v = 3t

b) To determine the time taken for the car to reach the final velocity, we can rearrange the previous equation:

t = \dfrac{v}{3}

Substituting the final velocity as the unknown v, we have:

t = \dfrac{v}{3}

c) To find the time it takes for the car to reach the midpoint of the distance, we can use the formula:

s = ut + \dfrac{1}{2}at^2

Since the car starts from rest, $u = 0$ . We can rearrange the equation to solve for time:

t^2 = \dfrac{2s}{a}

Substituting the values of s = 50 m (half of the total distance) and a = 3 m/s^2, we have:

t^2 = \dfrac{2 \cdot 50 \, \text{m}}{3 \, \text{m/s}^2}

Simplifying:

t^2 = \dfrac{100 \, \text{m}}{3 \, \text{m/s}^2}

t^2 = 33.33 \, \text{s}^2

t \approx 5.8 \, \text{s}

Therefore, it takes approximately 5.8 seconds for the car to reach the midpoint of the distance.

Please note that in this answer, we have rounded the final time to two decimal places.