kinematics (1 Viewer)

[pLuvia]

4. A particle is in oscillating motion obeying the law x=5cos2t. Find the velocity and acceleration at the points x=-5 and x=0

8. A particle passes a fixed point O and moves in a stragiht line with a velocity of (8+[1/3] t²) m/s, where t is the time in seconds after passing O. Find the distance travlled during the fourth second

 

[Riviet]

4. A particle is in oscillating motion obeying the law x=5cos2t. Find the velocity and acceleration at the points x=-5 and x=0

Find dx/dt and substitute x=-5 and 0 to find velocity at each of those points, then differentiate dx/dt and sub x=-5 and 0 again to find acceleration at each of these points.

 

[Riviet]

8. A particle passes a fixed point O and moves in a stragiht line with a velocity of (8+[1/3] t²) m/s, where t is the time in seconds after passing O. Find the distance travlled during the fourth second

Oo, i just figured out the second too lol. Just integrate 8+[1/3] t² and sub in t=4 to find the distance travelled.

 

[pLuvia]

But if I differentiate x=5cos2t there's no x after that

 

[pLuvia]

Yeh I did that way as well, but that's not the answer

I did that and got 352/9 but the answer is 109/9 ><"

 

[Templar]

But if I differentiate x=5cos2t there's no x after that

You differentiate with respect to t.

I did that and got 352/9 but the answer is 109/9 ><"

Travelled in the fourth second means the distance travelled from t=3 to t=4, so do a definite integral using those values.

 

[Riviet]

You differentiate with respect to t.

Exactly.

So you should get dx/dt = -10sin2t, and then just sub in the x values.