Question

The initial velocity of a truck is 10 m/s. How long must it accelerate at a constant acceleration of 2 m/s^2 before its average velocity is equal to three times its initial velocity?

Answer 1

Average velocity = initial velocity + final velocity / 2

We want to find how long it accelerate at a constant acceleration of 2 m/s² before its average velocity is equal to three times its initial velocity

Velocity average = Initial velocity +final velocity /2

3 × initial velocity = initial velocity + final velocity /2

Initial velocity = 10 m/s

3× 10 = 10+ final velocity /2

60 = 10 + final velocity

Final velocity = 50 m/s

Here acceleration (a) = 2 m/s²

Using equation of kinematics

Acceleration(a) = final velocity(V) - initial velocity (u)/time (t)

t = v-u /a = 50 - 10 / 2 = 40/2 = 20 sec

It will accelerate 20 sec, before its average velocity equal to 3 times initial velocity

Distance of travel = ut +1/2 at²

= 10×20 + 1/2× 2× 20×20 = 600 m long will travel