Question

Number 4 Question answer with explanation and steps

Answer 1

The time needed to accelerate and the time needed to decelerate are T1 and T2, respectively.

Together, they are the total time.

The acceleration multiplied by its time is 10 (T1).

The deceleration multiplied by its time is 20 (T2).

The velocity accelerated to is equal to the velocity decelerated from, so

V = a t

V = 10 T1

V = 20 T2

Again, the “accel to” and “decel from” velocities are equal, so 10 T1 = 20 T2

Therefore, T1 = 2 T2

Next, the total distance is the sum of the acceleration distance and the deceleration distance.

s = 1/2 at^2

200 m = 1/2 (accel rate) (T1)^2 + 1/2 (decel rate) (T2)^2

Substituting 2T2 for T1:

200 m = 1/2 (10) (2T2) ^2 + 1/2 (20) (T2)^2

200 m = 20 (T2) + 10 (T2)

200 m = 30 T2

T2 = 6.66 seconds

T1 = 2 T2 = 13.32 seconds

T1 + T2 = 19.98 seconds = total time