Name: Projectile Motion From a Height
Uploaded: 2019-07-19
Duration: 7 min 6 s
Description: In this video, let us analyse the projectile motion of an object thrown upwards at an angle from a height. Watch this video to learn more about this.

Question

The acceleration of a cart started at

t = 0

, varies with time as shown in the following figure. Find the distance traveled in

30 s

and draw the position-time graph.

Accepted Answer

We will first draw the velocity-time graph.

From the graph, we know that from $t = 0$ to $t = 10$ , the acceleration is constant and positive. So, the slope of $v - t$ curve should be $5 ft s^{- 2}$ .

From $t = 10$ to $t = 20 s$ , acceleration is zero. Hence, the slope of $v - t$ curve should be zero. That means the velocity will become constant.

From $t = 20$ to $t = 30 s$ , acceleration is negative but constant. So, the slope of $v - t$ curve should be $- 5 ft s^{- 2}$ .

Velocity at $t = 10 s$ ,

$v = u + a t = 0 + 5 (10) = 50 ft s^{- 1}$

Particle will have the same velocity till $t = 20 s$ .

Velocity at $t = 0$ ,

$v = u + a t = 50 + (- 5) 10 = 0$

So the $v - t$ curve should be:

We know that area of $v - t$ curve is the total distance of particle.

$∴$ Distance $= \frac{1}{2} (10 + 30) \times 50$

$= 1000 ft$ .

For displacement-time graph:

From $t = 0 t o t = 10 s$ , velocity is increasing. Hence, the slope of $x - t$ curve should be increasing.

From $t = 10$ to $20 s$ , velocity is constant. Hence, the slope of $x - t$ curve should be constant too.

From $t = 20$ to $30 s$ , velocity is decreasing. Hence, the slope must be decreasing.

So, $x - t$ curve should be drawn as below.

The acceleration of a cart started at $t = 0$ , varies with time as shown in the following figure. Find the distance traveled in $30 s$ and draw the position-time graph.

Important Questions on Rest and Motion : Kinematics

Learn and Prepare for any exam you want !

The acceleration of a cart started at t=0, varies with time as shown in the following figure. Find the distance traveled in 30 s and draw the position-time graph.

Important Questions on Rest and Motion : Kinematics

Learn and Prepare for any exam you want !

The acceleration of a cart started at $t = 0$ , varies with time as shown in the following figure. Find the distance traveled in $30 s$ and draw the position-time graph.