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A car accelerates from 5 m/s to 21 m/s at a rate of 3 m/s² How far does it travel while accelerating?

User Wbyoung
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Final answer:

The car accelerates from 5 m/s to 21 m/s at a rate of 3 m/s² and travels a distance of approximately 69.24 meters during this acceleration.

Step-by-step explanation:

To determine how far the car travels while accelerating, we can use the kinematic equation for uniformly accelerated motion, which is:

x = v0t + ½at²

However, we don't have the time (t) of the acceleration directly given. To find this, we can use the formula that relates velocity, acceleration, and time:

v = v0 + at

Here, v is the final velocity (21 m/s), v0 is the initial velocity (5 m/s), and a is the acceleration (3 m/s²). Rearrange this equation to solve for time (t):

t = (v - v0) / a

After finding the time, we can plug it back into the first equation to get the displacement (x).

Let's calculate the time first:

t = (21 m/s - 5 m/s) / 3 m/s²
= 16 m/s / 3 m/s²
= 5.33 s

Now, using the time value in the first equation:

x = (5 m/s)(5.33 s) + ½(3 m/s²)(5.33 s)²
= 26.65 m + ½(3 m/s²)(28.39 s²)
= 26.65 m + 1.5 m/s² × 28.39 s²
= 26.65 m + 42.59 m
= 69.24 m

The car travels 69.24 meters while accelerating.

User Shahzad Qureshi
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