# PhysicsVelocity time graph help

#### Jerome

##### New member
A train starts from rest from a station and travels with uniform acceleration 0.5m/s^2 for 20s. it travels with uniform velocity for another 30s, the brakes are then applied so that a uniform retardation is obtained and the train comes to rest in a further 10s. sketch the velocity-time graph of this motion. Using your graph, calculate the total distance travelled by the train

please can i see the graph, and also include explanation so that i can understand better

#### MarkFL

Staff member
First, let me ask you if the velocity changes uniformly, that is, the acceleration is constant, how will the velocity vary, mathematically speaking?

#### Jerome

##### New member
i don't have answers to that.

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Welcome to MHB, Jerome!

A train starts from rest from a station and travels with uniform acceleration 0.5m/s^2 for 20s. it travels with uniform velocity for another 30s, the brakes are then applied so that a uniform retardation is obtained and the train comes to rest in a further 10s. sketch the velocity-time graph of this motion. Using your graph, calculate the total distance travelled by the train

please can i see the graph, and also include explanation so that i can understand better
i don't have answers to that.
The formula for velocity with uniform acceleration is:
$$v = v_0 + a t$$
where $v$ is the speed at time $t$, $v_0$ is the initial speed, and $a$ is the uniform acceleration.

Is this formula known to you?

Anyway, in your problem, we can deduce that $v_0 = 0$, since the train is initially at rest.
And $a=0.5 m/s^2$ is given.

Do you know how to draw the graph of $v=0.5 t$ for the time period of 0 to 20s?
What will be the speed at $t=20s$?

#### Jerome

##### New member
Welcome to MHB, Jerome!

The formula for velocity with uniform acceleration is:
$$v = v_0 + a t$$
where $v$ is the speed at time $t$, $v_0$ is the initial speed, and $a$ is the uniform acceleration.

Is this formula known to you?

Anyway, in your problem, we can deduce that $v_0 = 0$, since the train is initially at rest.
And $a=0.5 m/s^2$ is given.

Do you know how to draw the graph of $v=0.5 t$ for the time period of 0 to 20s?
What will be the speed at $t=20s$?

i got that thanks, the graph looks like a trapezium, so the area of the trapezium is the total distance right?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
i got that thanks, the graph looks like a trapezium, so the area of the trapezium is the total distance right?
Yep!