Equations of Motion

A particle moves a long the  $x-$  axis. The function  $x\left(t\right)$  gives the particle's position at any time,  $t\ge0$  :  $x\left(t\right)=5t^2-12t+3.$  What is the particle's velocity  $v\left(t\right)$  at  $t=3$  seconds?

• 18

• 78

• 42

• 102

A particle moves a long the  $x-$ axis. The function  $x(t)$ gives the particle's position at any time,  $t≥0$  :   $x(t)=5t^2−12t+3.$  What is the direction of the particle's motion at  $t=3$  ?

• Left

• Right

• Up

• Non f the above.

A particle moves along the  $x-$  axis . The function  $x(t)$  gives the particle's position at any time  $t≥0$ ,  $x(t)=2t^2-3t+5$  . What is the particle's acceleration  $a(t)$  at  $t=1$  ?

• 1  $ms^{-2}$  

• 2  $ms^{-2}$  

• 3 $ms^{-2}$  

• 4  $ms^{-2}$  

A large stone is falling through a layer of mud. At time t
t seconds, the depth of the stone in metres below the surface is given by:  $x\left(t\right)\ =\ 20\ \left(1-e^{\frac{-t}{2}}\right)$  . What is $\frac{\text{d}v}{\text{d}t}$  ?

•  $5\ e^{\frac{-t}{2}}$  

•  $-20\ e^{\frac{-t}{2}}$  

•  $10\ e^{\frac{-t}{2}}$  

•  $-5e^{\frac{-t}{2}}$  

Given that the velocity  $v\left(t\right)$  of the particle is given by  $v\left(t\right)=\sin\ \left(\frac{\pi t}{2}\right).\$  If initially the particle has a no displacement. What is the position of the particle at time t=1?

• 0

•  $\frac{\pi}{2}$  

•  $-\frac{\pi}{4}$  

•  $\frac{\pi}{3}$  

Acceleration is defined as

The following is the assumption taken when deriving Newton's equation of Motion.

• Displacement is constant.

• Velocity is Constant.

• Acceleration is constant.

• Time is constant.

The distance taken by the particle at a constant acceleration is the same as the area under;

• Velocity-time graph

• Acceleration-time graph

• Displacement-Time graph

• None of the above

The velocity-time graph of a DES II student moving along a straight line is given below. Find his average velocity.

• $3.33\ \ ms^{-1}$

• $6.67\ ms^{-1}$

• $5\ ms^{-1}$
  

• $100\ \ ms^{-1}$

Write all the terms used in the equations of motion (Separate all of them by commas and finally by "and". Use one word for each stated term).