A particle is moving with acceleration a ( t ) = 18 t + 16 . Its position at time t = 0 is s ( 0 ) = 10 and its velocity at time t = 0 is v ( 0 ) = 16 . What is its position at time t = 8 ?

Step-by-step explanation:

A particle is moving with acceleration modeled by the function:

We are given that its position s(t) at t = 0 is 10 and that its velocity v(t) at t = 0 is 16.

And we want to find its position at t = 8.

Velocity is the integral of the acceleration. Hence:

Find the velocity. Remember the constant of integration!

Since v(t) is 16 when t = 0:

Hence, our velocity is given by:

Position is the integral of the velocity. Hence:

Integrate:

s(t) is 10 when t = 10. Hence:

So, our position function is:

The position at t = 8 will be:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west