Particle Motion

A particle moves along the x-axis. At which time on the velocity versus time graph particle farthest left of its starting point?

• A

• B

• C

• D

• E

The position of a particle on a line is given by x(t) = x³-t, t≥0. Find the distance traveled by the particle in the first two seconds.

• 0.385

• 3.385

• 6

• 6.385

• 6.770

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

If x(t) is the position of the object at time t, and a(t) is the acceleration of the object at time t, which of the following is true?

• v(5)>v(2)

• x(5)>x(2)

• a(6)>a(2)

• x(10)<x(5)

• a(9)>a(6)

Tags

CCSS.HSF.IF.B.4

A particle moves along the x-axis so that at time t≥0 its position is given by x(t) = 2t³-21t²+72t-53. At what time t is the particle at rest?

• t=1 only

• t=3 only

• t=7/2

• t=3 and t=7/2

• t=3 and t=4

Tags

CCSS.HSA.APR.B.3

A particle moves along a straight line. The graph of the particle's position x(t) at time t is shown above for 0<t<6. The graph has horizontal tangents at t=1 and t=5 and a point of inflection at t=2. For what values of t is the velocity of the particle increasing?

• 0<t<2

• 1<t<5

• 2<t<6

• 3<t<5 only

• 1<t<2 and 5<t<6

A particle moves along the x-axis with velocity given by v(t)=3t²+6t for time t≥0. If the particle at position x=2 at time t=0, what is the position of the particle at time t=1?

• 4

• 6

• 0

• 11

• 12

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

The velocity of a particle moving on a line at time t is v=3t^1/2+5t^3/2 meters per second. How many meters did the particle travel from t=0 to t=4?

• 32

• 40

• 64

• 80

• 184

If the position of a particle on the x-axis at time t is -5t², then the average velocity of the particle for 0≤t≤3 is

• -45

• -30

• -15

• -10

• -5

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

A particle travels in a straight line with a constant acceleration of 3 meters per second per second. If the velocity of the particle is 10 meters per second at time 2 seconds, how far does the particle travel during the time interval when its velocity increases from 4 meters per second to 10 meters per second?

• 20 m

• 14 m

• 7 m

• 6 m

• 3 m

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.2

A particle moves along the x-axis so that any time t≥0, its velocity is given by v(t)3+4.1cos(0.9t). What is the acceleration of the particle at time t=4?

• -2.016

• -0.677

• 1.633

• 1.814

• 2.978