A 2-kg object has a velocity given by v = (3.0 m/s)i + (4 m/s²t) j

a) what is the speed of the object at t = 0 s ?

b) what is the speed of the object at t = 1 s ?

c) what is the angle between the velocity and the x-axis at t = 1 s?

d) what is the acceleration of the object at t = 2 s ?

e) what is the net force on the object t = 2 s ?

a) at t = 0 we have   v = (3 m/s)i  

The speed is the magnitude of this vector, i.e. 3 m/s

b) v(t=1s) = (3 m/s)i + (4 m/s)j

The speed is the magnitude of this vector, i.e.

[( 3 m/s)² + (4 m/s)²]^1/2 = 5 m/s

c) The angle between the velocity and the x-axis is

= tan^-1(4/3) = 53.1°

d) to get the acceleration, we differentiate the velocity

a = dv/dt = 4 m/s²j

This does not depend on t, so is true at any time, not just at t=2 s. Note that acceleration is a vector, so we must specify the direction, done here using the unit vector j.

e) F = ma

= (2 kg)(4 m/s²)j

= 8 N j

again, since force is a vector, we have specified the direction as well as its magnitude.