A Jeep accelerated at 2.2 m/s2 until after 18 seconds its displacement was 660 meters. Assuming the Jeep traveled in a straight line, calculate the initial velocity.

Respuesta :

Ok so we know:
The time (t) is 18seconds
The acceleration (a) is 2.2m/s2
The displacement (r) is 660

Using the equation
[tex]r = ut + \frac{1}{2} a {t}^{2} [/tex]
With 'u' being the initial velocity we want, we get:
[tex]660 = 18u + 356.4[/tex]
So:
[tex]18u = 303.6[/tex]
So:
[tex]u = 16.8666[/tex]
So the original/initial velocity was 16.8666 or 16.87 m/s

Hope this helped

The initial velocity of the Jeep is 16.87 m/s

From one of the equations of kinematics for linear motion

We have that

[tex]s = ut + \frac{1}{2}at^{2}[/tex]

Where s is the distance or displacement

u is the initial velocity

a is the acceleration

and t is the time

From the question,

a = 2.2 m/s²

t = 18 secs

s = 660 meters

Putting the above parameters into the formula, we get

[tex]660 = (u \times 18) + \frac{1}{2} \times 2.2 \times 18^{2}[/tex]

[tex]660 = 18u + 1.1 \times 324[/tex]

[tex]660 = 18u + 356.4[/tex]

∴ [tex]18u = 660 -356.4[/tex]

[tex]18u = 303.6[/tex]

Divide both sides by 18

[tex]\frac{18u}{18}=\frac{303.6}{18}[/tex]

∴ u = 16.87 m/s

Hence, the initial velocity of the Jeep is 16.87 m/s

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