Kinematics

What quantities can be obtained directly from a displacement time graph?

• Displacement and time

• Displacement, time and acceleration

• Displacement, time and speed

• Displacement, time and velocity

The velocity of a particle is given by  $v=4-\frac{16}{\left(t+1\right)}$  . What is the expression for it's acceleration

•  $a=-\frac{16}{\left(t+1\right)^2}$  

•  $a=4t-16\ \ln\left(t+1\right)$  

•  $a=\frac{16}{\left(t+1\right)^2}$  

•  $a=16t$  

A particle has acceleration  $a=\frac{16}{\left(t+1\right)^2}$  . At what time is the acceleration equal to  $0.25\ m\ s^{-2}$  ?

•  $t=8\ s$  

•  $t=7\ s$  

•  $t=6\ s$  

•  $t=0$  

A particle travels in a straight line so that, t s, after passing through a fixed point O, its velocity, v m/s is given by

 $v=4e^{2t}-24t$  
What is the distance travelled by the particle in the third second?

• 638 m

• 699 m

• 61 m

• 700 m

A particle moves in a straight line so that, t s after passing through a fixed point O, its velocity, v m/s is given by

 $v=2t-11+\frac{6}{t+1}$  .
What is the acceleration of the particle when it is at instantaneous rest?

•  $\frac{11}{6}$  

•  $2$  

•  $\frac{13}{6}$  

•  $\frac{17}{6}$  

A body moves in a straight line such that, t seconds after passing a fixed point, its acceleration, a m/s2 is given by

 $a=3t^2+6$ . When t=0, the velocity of the body is 5m/s. What is the velocity when t=3?

• 25 m/s

• 50 m/s

• 75 m/s

• 45 m/s

The acceleration of a particle a m/s2, at time t seconds is given by

 $a=6-2t$ . When t=0, the particle is at rest at a point 4 m from the origin O.
When is the particle next at rest and what is it's displacement from O at that time? 

• t=6 s, s=36 m

• t=6 s, s=40 m

• t=3 s, s=40 m

• t=3 s, s=36 m

A particle starts from rest and moves in a straight line so that, t seconds after leaving a fixed point O, its velocity, v m/s, is given by

 $v=4+8\cos2t$  
What is the range of values of the velocity?

•  $4\le v\le8$  

•  $-8\le v\le4$  

•  $-4\le v\le12$  

•  $-12\le v\le4$  

A particle starts from rest and moves in a straight line so that, t seconds after leaving a fixed point O, its velocity, v m/s, is given by

 $v=4+8\cos2t$  
What is the range of values of acceleration

•  $0\le a\le16$  

•  $-4\le a\le12$  

•  $-16\le a\le16$  

•  $-8\le a\le12$  

A particle starts from rest and moves in a straight line so that, t seconds after leaving a fixed point O, its velocity, v m/s, is given by

 $v=4+8\cos2t$  
What is the distance travelled during the time interval
 $0\le t\le\frac{\pi}{2}$  

• 6.28 m

• 7.65 m

• 9.02 m

• 12.57 m