What is the displacement of a car with an acceleration of 4.00 m/s2 as it increases. its speed from 10.0 m/s to 30.0 m/s ?

100 m.

Explanation:

The following data were obtained from the question:

Initial velocity (u) = 10 m/s

Final velocity (v) = 30 m/s

Acceleration (a) = 4 m/s²

Displacement (D) =?

Next, we shall determine the time.

This can be obtained as follow:

Acceleration is defined as the rate of change of velocity with time. Mathematically, it is expressed as:

a = (v – u) / t

Where

a is the acceleration.

u is the initial velocity.

v is the final velocity.

t is the time.

With the above formula, we can obtain the time as follow:

Initial velocity (u) = 10 m/s

Final velocity (v) = 30 m/s

Acceleration (a) = 4 m/s²

Time (t) =?

a = (v – u) / t

4 = (30 – 10)/t

4 = 20/t

Cross multiply

4 × t = 20

Divide both side by 4

t = 20/4

t = 5 secs.

Finally, we shall calculate the displacement of car as illustrated below:

Velocity is defined as rate of change of displacement with time. Mathematically, it can be expressed as:

(v – u) = D/ t

Where:

u is the initial velocity.

v is the final velocity.

t is the time.

D is the displacement.

With the above formula, we can calculate the displacement of the car as follow:

Initial velocity (u) = 10 m/s

Final velocity (v) = 30 m/s

Time (t) = 5 s.

Displacement (D) =?

(v – u) = D/ t

(30 – 10) = D/5

20 = D/5

Cross multiply

D = 20 × 5

D = 100 m

Therefore, the displacement of the car is 100 m