Question

A car moves with an initial velocity of 19 m/s due north. (Part A) Find the velocity of the car after 5.6 s if its acceleration is 1.6 m/s^2 due north. (Part B) Find the velocity of the car after 5.6 s if its acceleration is 1.5 m/s2 due south.

Answer 1

For Part A, the car's final velocity is 27.96 m/s due north after 5.6 seconds with an acceleration of 1.6 m/s² due north. For Part B, the car's final velocity is 10.6 m/s due north after 5.6 seconds with an acceleration of 1.5 m/s² due south.

Step-by-step explanation:

Calculating Final Velocity with Acceleration

Part A: To find the velocity of the car after 5.6 seconds with an acceleration of 1.6 m/s2 due north, we need to use the formula final velocity (v) = initial velocity (u) + acceleration (a) × time (t). For this scenario:

Acceleration (a) = 1.6 m/s2

Time (t) = 5.6 s

So the final velocity would be:

Time (t) = 5.6 s

The final velocity can be calculated as:

v = 19 m/s + (-1.5 m/s2 × 5.6 s) = 19 m/s - 8.4 m/s = 10.6 m/s due north.

Answer 2

Assuming

east is the positive x direction

north is the positive y direction

initial velocity , u = 19 j m/s

a) acceleration , a = 1.6 j m/s^2

Using first equation of motion

v = u + a × t

v = 19 + 5.6× 1.6

v = 28 j m/s

the velocity of the car after 5.6 s is 28 m/s north

b)

acceleration , a = -1.5 j m/s^2

Using first equation of motion

v = u + a × t

v = 19 - 5.6 ×1.5

v = 10.6 j m/s

the velocity of the car after 5.6 s is 10.6 m/s north