Question

“A body has an initial position xin = +2 m, an initial velocity vin = 1 m/s and accelerates with an acceleration a = -1 m/s^2

Its average velocity in m/s for the time interval from t = 2 s to t = 4 s is:”

A) 2

B) 1

C) -2

D) -1

I found 3 different solutions to this question on Chegg, one used derivatives and the other didn’t so please help with an expert answer.

Answer 1

For uniform acceleration, s=ut+1/2 at2, where s is displacement, u is initial velocity, a is acceleration and t is time.

Here, u =1 m/s, a = -1 m/s2 , t=2 s.

So,s= 1*2+1/2*(-1)*2*2 = 0 m.

So, displacement in first 2 seconds is 0 m.

Similarly, for u=1 m/s, a = -1 m/s2 and t= 4 s, s=1*4+1/2(-1)*4*4 = - 4 m.

So, displacement in first 4 seconds is - 4 m.

So, displacement from t=2 s to t=4 s is equal to : - 4 m - 0 m = - 4 m.

Now, time interval between t=2 s to t=4 s is 4-2 = 2 seconds.

So, average velocity = (displacement)/time = -4 /2 = -2 m/s.

So, option C is correct.