Question:

A car travels along a straight road. At time t=0, the car is at rest and begins to accelerate uniformly at a rate of 2 m/s². After 10 seconds, the car's velocity has reached 20 m/s.

a) What is the car's initial velocity?
b) How far does the car travel during the first 10 seconds?
c) How long does it take the car to come to a stop?

Answer:

a) To find the car's initial velocity, we can use the formula for uniformly accelerated motion:

v = u + at

Where: v = final velocity = 20 m/s
u = initial velocity
a = acceleration = 2 m/s²
t = time = 10 s

Rearranging the equation to solve for u:

u = v - at

Substituting the given values:

u = 20 m/s - (2 m/s²)(10 s)
u = 20 m/s - 20 m/s
u = 0 m/s

Therefore, the car's initial velocity is 0 m/s.

b) To find the distance traveled during the first 10 seconds, we can use the formula for displacement during uniformly accelerated motion:

s = ut + (1/2)at²

Where: s = displacement
u = initial velocity = 0 m/s
a = acceleration = 2 m/s²
t = time = 10 s

Substituting the given values:

s = (0 m/s)(10 s) + (1/2)(2 m/s²)(10 s)²
s = 0 m + (1/2)(2 m/s²)(100 s²)
s = 0 m + (1/2)(200 m)
s = 0 m + 100 m
s = 100 m

Therefore, the car travels a distance of 100 meters during the first 10 seconds.

c) To find the time it takes for the car to come to a stop, we need to determine when the velocity becomes zero. We can use the formula:

v = u + at

Where: v = final velocity = 0 m/s
u = initial velocity = 0 m/s
a = acceleration = 2 m/s²
t = unknown time

Rearranging the equation to solve for t:

t = (v - u) / a

Substituting the given values:

t = (0 m/s - 0 m/s) / 2 m/s²
t = 0 s / 2 m/s²
t = 0 s

Therefore, it takes 0 seconds for the car to come to a stop.

In summary: a) The car's initial velocity is 0 m/s. b) The car travels a distance of 100 meters during the first 10 seconds. c) It takes 0 seconds for the car to come to a stop.