A particle P moves with acceleration (-3i + 12j) m/s^2. Initially the velocity of P is 4i m/s. (a) Find the velocity of P at time t seconds. (b) Find the speed of P when t = 0.5

Solution:

1. V = V(0) + a*t

2. From the question: a = (-3i + 12j); V(0) = 4i

3. V at time t seconds:

V = 4i + (-3i+12j)*t

4. V = 4i + (-3ti + 12tj)

5. V = 4i – 3ti + 12 tj m/s

*Bold letters are vectors

Answer: velocity of P at time t seconds is V = 4i – 3ti + 12 tj m/s

1. t = 0.5

2. from a) we know that at any given t velocity is V = 4i – 3ti + 12 tj

3. V = 4i – 30.5i + 120.5j

4) V = 4i – 1.5*i + 6*j = 2.5i + 6j

5. speed, S, is a scalar, then:

S = |V|= sqrt (2.5^2 + 6^2) = 6.5 m/s

Answer: 6.5 m/s