Acceleration Time Graphs

Description:

The Concept

Acceleration – Time graphs display the motion of a particle by showing the changes of velocity with respect to time.

For Example,

Above acceleration – time graph represents an object moving with uniform acceleration

Above acceleration – time graph represents particle going at uniform acceleration in positive direction until, t = t₁, when it starts moving with uniform velocity. From t = t₂, the object has negative acceleration and it is velocity starts to retard.

Salient Points

Velocity – Time graphs are also called a − t graphs.

Slope of Velocity – Time graph gives a quantity called Jerk.

• Slope of any curve = dy/dx(Revisit Differential Calculus for more details)

• Slope of acceleration - time graph = da/dt = jerk

• It doesn’t have much applications in Kinematics.

Area under the Velocity – Time graph gives Change in Velocity.

• Area under any curve = x₂∫x₁ f(x) . dx

• Area under acceleration - time graph = t₂∫t₁ a . dt = velocity

Example Problem 2

Find the final velocity of the object if it started at v = 5 m/s.

We know area under the curve of a − t graph gives velocity.

Area = 1/2 × 20 × 5 + 20 × 5 + 1/2 × 20 × 5 = 200 m/s

Therefore,

Final Velocity = Initial Velocity + Change in Velocity

Final Position = 5 + 200 = 250 m/s