Question: A car moving along a straight road has an initial velocity of 10 m/s. It accelerates uniformly at a rate of 2 m/s² for a distance of 50 meters.

a) Determine the final velocity of the car. b) Calculate the time it takes for the car to travel this distance. c) Find the average acceleration of the car during this time interval.

Answer: a) To determine the final velocity, we can use the following equation:

v = u + at

where:

• v is the final velocity
• u is the initial velocity
• a is the acceleration
• t is the time interval

Given data: u = 10 m/s a = 2 m/s²

Plugging these values into the equation, we have:

v = 10 m/s + (2 m/s²)(t)

Since we're interested in the final velocity when the car has traveled a distance of 50 meters, we can substitute t with the time it takes to cover that distance. Rearranging the equation for time, we get:

t = (v - u) / a

t = (v - 10 m/s) / (2 m/s²)

Now, we can substitute this expression for time back into the equation for velocity:

v = 10 m/s + (2 m/s²) * [(v - 10 m/s) / (2 m/s²)]

Simplifying this equation, we have:

v = 10 m/s + v - 10 m/s

2v = 10 m/s

v = 5 m/s

Therefore, the final velocity of the car is 5 m/s.

b) To calculate the time it takes for the car to travel a distance of 50 meters, we'll use the following equation:

s = ut + (1/2)at²

where:

• s is the distance
• u is the initial velocity
• a is the acceleration
• t is the time interval

Given data: s = 50 m u = 10 m/s a = 2 m/s²

Plugging in these values, we have:

50 m = (10 m/s)t + (1/2)(2 m/s²)t²

Simplifying and rearranging the equation, we have a quadratic equation:

t² + 5t - 50 = 0

(t + 10)(t - 5) = 0

Therefore, t = -10 or t = 5. Since time cannot be negative in this context, the car takes 5 seconds to travel a distance of 50 meters.

c) The average acceleration of the car during this time interval can be calculated using the formula:

average acceleration = (change in velocity) / (time interval)

Given data: Initial velocity (u) = 10 m/s Final velocity (v) = 5 m/s Time interval (t) = 5 s

Substituting these values into the formula, we have:

average acceleration = (5 m/s - 10 m/s) / (5 s)

Simplifying the equation, we get:

average acceleration = -5 m/s / 5 s

average acceleration = -1 m/s²

Therefore, the average acceleration of the car during this time interval is -1 m/s².