Time-Dependent Force: Solving for Speed & Displacement

[bolivartech]

Homework Statement

A time-dependent force, F = (8.00i – 4.00tj) N, where t is in seconds, is exerted on a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s? (b) How far is the object from its initial position when its speed is 15.0 m/s? (c) Through what total displacement has the object traveled at this moment?

Homework Equations

F = ma
a = d/t

The Attempt at a Solution

(a)
F = ma

(8.00i – 4.00tj) N = (2.00 kg)(15.0 m/s)

t = 2s


(b)
a = d/t

(15.0 m/s2)(t) = d

I don't see why it's not 2 seconds. Is it not just algebra, did I leave out a significant part of the equation? Thanks, this site has taught me quite a bit.

 

[rl.bhat]

F = ma = (8i - 4jt) N. m is given. So
a = 4i - 2jt. You can write a = dv/dt. So
dv = 4i*dt - 2jt*dt.
Take integration with respect to time.
v = 4i*t - jt^2 + C. When t = 0 , vo = 0. So C = 0.
The magnitude of v is given
And v^2 = (4t)^2 + t^4
Put the value of v and solve for t.