A car is traveling due north at 23.6 m>s. Find the velocity of the car after 7.10 s if its acceleration is (a) 1.30 m>s2 due north, or (b) 1.15 m>s2 due south.

a) v = 32.8 m/s

b) v= 15.4 m/s

Explanation:

a)

Applying the definition of acceleration (assumed to be constant), we can write the following expression for the velocity v:

       

        where v₀ is the initial velocity and a is the acceleration, being t the

       time elapsed.

In the case a) the acceleration and the velocity vectors have both the same direction (due north), so both have the same sign, which means that the car is speeding up.Replacing by the givens v₀ and t in (1), we get:

       

b)  

In this case, the acceleration vector and the velocity vector have opposite directions, so the car slows down, due to both vectors have opposite signs.Replacing by the givens in (1) and taking into account the signs, we get:

       

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