Question

how do you find velocity and distace travelled from an acceleration time. graph? (given: Vo=0, car is moving in straight direction) graph is a piecewise { y=-x [0,5] and y=0 [5,infinity] }

Answer 1

Finding velocity from acceleration time graph : Calculate the total area under the curve . Area under the curve will give you change in velocity or velocity if initial velocity is zero.

Finding distance ; Plot velocity-time graph from acceleration-time graph. Calculate area under the velocity-time graph. This will give you change in position. For distance calculation, at each turning point of curve calculate area separately, remove all negative signs and add all of them.

As given in question,

From the acceleration time graph,

change in velocity = 0.50x 5 x 5 = 12.5 m/s

or, v_f - v₀ = 12.5 m/s

or, v_f = 12.5 m/s (Given, v₀ = 0 m/s)

For plotting velocity - time graph,

we know that

  

According to plot , a = -t

so, ; t >0

so the velocity time graph is a parabola.

For distance calculate the area under v-t curve or just integrate (for this c ase)   ​

so in t = 5 seconds distance covered by the car is

  

  

NOTE: The negative sign in acceleration and velocity is showing that the motion is in negative x direction.

For doubt please comment.