Question

Numerical related to the second equation of motion

Answer 1

The second equation of motion is :

S=ut+1/2at(t) where is "s" is distance, u is initial velocity, a is acceleration and t is time.

Example 1

A bus starts from rest and accelerates at a rate of 2.5 m/s2 for a time of 50 s. Determine the distance travelled by the bus during the acceleration phase.

Now let us identify the different variables involved.

u the initial speed = 0 m/s

t time taken = 50 s

a acceleration = 2.5 m/s2

s distance travelled = ???

If we want calculate s the distance travelled we will have to use the second equation of motion

S = ut + 1/2at2

Substituting the different values we get

S = ut + 1/2at2

= o*50 + 0.5*2.5 *502

= 0 + 1.25*2500

=3125 m

Example 2

An aero plane travelling at a speed of 300 m/s lands on a track 2000 m long and decelerates for a time of 25 s until it comes to rest. Calculate the deceleration needed to stop the plane.

We must now identify the different variables involved as in the first example.

initial speed u = 300 m/s

time taken t = 25 s

Distance travelled s = 2000 m

acceleration a = ????

If we want calculate the acceleration a we will have to use the second equation of motion

S = ut + 1/2at2

and make a the subject of formula.

s – ut = 1/2at2

a =2(s - ut)/t2

= 2(2000 – 300*25)/252

= –8.8 m/s2

Do tell if u want more examples

Hope this helps