How to calculate acceleration and deceleration

Question

I have a car with speed x, and can accelerate at a rate of 0.5 m/s^2, and can decelerate at a rate of -0.1 m/s^2. Maximum speed is 20 m/s.

To accelerate the car speed, at each frame I need to do:

car.CurrentSpeed = car.CurrentSpeed + 0.5

To decelerate the car speed, at each frame I need to do:

car.CurrentSpeed = car.CurrentSpeed - 0.1

Is this correct?

I have found this answer which suggest the following speed formula:

Speed += ((MoveDirection * MaximumSpeed) - Speed) * AccelerationFactor

Where:

• Speed is the current speed the entity is travelling at on the current axis.
• MoveDirection is the direction the entity is trying to travel in on the current axis, 1 is forward, 0 is still and -1 is backwards. All values in between are allowed.
• MaximumSpeed is a constant determining the fastest that the entity can travel on the current axis.
• AccelerationFactor is a constant between 0 and 1 that represents the rate of acceleration and deceleration. 1 is instant, and 0 will never move.

Using the same formula then:

To accelerate:

car.CurrentSpeed += ((MoveDirection * 20) - car.CurrentSpeed) * 0.5

What would be the move direction? Can it be the heading?

Answer 1

move direction is the heading. You have to distinguish speed from velocity; when you multiply speed (a scalar) with the move direction (a unit vector), you get the velocity, which is a vector.

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Your assumptions show a flaw:

You don't take the time into consideration.

If your speed is based on m/s and your acceleration is in m/s^2, at each frame you should do something like:

car.CurrentSpeed = car.CurrentSpeed + (0.5 * delta_time)

and to decelerate, you need to reduce the speed:

car.CurrentSpeed = car.CurrentSpeed - (0.1 * delta_time)

where delta_time is the time for each frame.

This will take the frame-rate into consideration.

To cap the speed at it's maximum:

car.CurrentSpeed = min( maximum_speed, car.CurrentSpeed + (0.5 * delta_time) )

You can then apply this speed to the heading direction, you'll get the velocity vector (if you need it).

Now be aware that if you brake your speed will need to be capped to zero:

car.CurrentSpeed = max ( zero, car.CurrentSpeed - (0.1 * delta_time) )

...as opposed to if you reverse, where your reverse speed will need to defined differently. Now it's either going to be a positive speed with a flag that says you're in reverse, or a negative speed; this will depend on the rest of your architecture.