Question

Objects A and B both start at rest. They both accelerate at the same rate. However, object A accelerates for 3x the time as object B. What is the final speed of object A compared to that of object B

Answer 1

v_Object A = 3v_Object B

OR

1/3v_Object A = v_Object B

Step-by-step explanation:

Let's see what variables we have in this problem.

Since the objects both start at rest, we have an initial velocity of 0 m/s.

The objects accelerate, so we will have acceleration.

Object A accelerates for 3x the time as Object B, so we have time.

The problem wants us to compare their final speeds, so we have final velocity.

Check what constant acceleration kinematic equation has these variables:

• v = v₀ + at

Let's create values for the unknown variables and compare the final velocities.

• v = ?
• v₀ = 0 m/s (objects start at rest)
• a = 5 m/s²
• t = 10 s

Since Object A accelerates for 3x the time as Object B, we can use t = 30 s for Object A.

Let's write the two equations:

1. v = (0) + (5)(10)
2. v = (0) + (5)(30)

Simplify these equations.

1. v = 50 m/s
2. v = 150 m/s

Let's use another set of values to compare the final velocities to see if the velocities differ by 100 m/s or Object A has 3x the final velocity of Object B.

• v = ?
• v₀ = 0 m/s (objects start at rest)
• a = 3 m/s²
• t = 7 s

Write the two equations:

1. v = (0) + (3)(7)
2. v = (0) + (3)(21)

Simplify these equations.

1. v = 21 m/s
2. v = 63 m/s

Now we can clearly see that the final velocities are differed by 3x. Object A has 3x the final speed compared to that of Object B.