A researcher observes a vehicle with an initial velocity of 14 m/s. The vehicle accerlerates uniformly with an accerleration of 3 m/s². After 6 seconds, what is the velocity of the vehicle?

Question

Physical Science

Answer 1

As in Algebra, the slope-intercept form of the equation of the line is y = m+b.

b = 14, m = 3

v(t)= v₀ + a*t

Velocity = 14 m/sec + (3 m/sec²)(x sec)

So, find ;y when x=6.

Answer 2

Write initial velocity as v₀ = 14 meters per second or 14 (m/s).

Write velocity in 6 seconds as v₆ equal to 14 (m/s) at start of timing plus an increase in velocity of 3 meters per second every single second (m/s²) throughout the timing (s); that is to say, v_{6 =} 14 (m/s) + 3 (m/s²) × 6 (s).

In dimensional analysis, meters per second every second (m/s²) times seconds (s) is written as (m/s²) × (s) or (m×s)/(s×s) which simplifies to (m/s) by crossing out an "s" in the numerator and denominator of the division fraction.

So, finally, velocity after 6 seconds (v₆) equals initial velocity (v₀) plus uniform acceleration (a) times time of travel (t).

v₆ = v₀ + at or v₆ = 14 (m/s) + (3 m/s²)(6 s), which gives 14 (m/s) + 18 (m/s) or 32 (m/s).

Answer 3

Gloria,

for a constant acceleration the velocity of a body is: v(t)= v₀ + a*t where v₀ is the initial velocity and a is the acceleration.

In your case v₀ =14 m/s and a=3 m/s² and t=6 s.

Does this help?

Jim