Question
For t≥ 0 , the velocity of a particle moving along the x-axis is given by \(v(t)=t^{3}-6t^{2}+10t-4\). At what time t does the direction of motion of the particle change from right to left?
A 0.586
B 1.184
C 2.000
D 2.816
Answer/Explanation
Question
A particle moves along the x-axis. The graph of the particle’s velocity v(t) at time t is shown above for 0<t<4.5. How many times does the particle change direction over the time interval 0<t<4.5 ?
A Two
B Three
C Five
D Seven
Answer/Explanation
Ans:A
Question
A particle moves along the x-axis so that at time t≥0 its position is given by \(x(t)=2t^{3}-9t^{2}-60t+4\). What is the total distance traveled by the particle over the time interval 0≤t≤7 ?
A 168
B 171
C 175
D 375
Answer/Explanation
Ans:D
Question
A particle moves along the y-axis so that at time t≥0 its position is given by \(y=\frac{2}{3}t^{3}-5t^{2}+8t\). Over the time interval 0<t<5, for what values of t is the speed of the particle increasing?
A 2.5<t<5
B 4<t<5 only
C 0<t<1 and 4<t<5
D 1<t<2.5 and 4<t<5
Answer/Explanation
Ans:D
The velocity of the particle is given by
\(y'(t)=2t^{2}-10t+8=2(t−1)(t−4)\),