1.If a body moves in a straight line according to the law s= 24t +3t^2 - t³, where s is the distance measured in meters from the origin and t is the time in seconds after it starts to move, calculate the body’s velocity as a function of time.

Question

1.If a body moves in a straight line according to the law s= 24t +3t^2 - t³, where s is the distance measured in meters from the origin and t is the time in seconds after it starts to move, calculate the body’s velocity as a function of time.

a.v = 30t – 3t²
b.v= 30t - t²
c.v = 24 + 3t- t^2
d.v = 24 +6t -3t²

I think it's D but also confused by A

2.what is the velocity of the body in question 10 when t = 3seconds?

a.15 m/s
b.27 m/s
c.63 m/s
d.81 n/s

I think it's A but confused it might by C.

can you help me .

Answer 1

1) D

2) v = 24 +6t -3t²
when t = 3
v = 24 +18 - 27
v = 15 or in other words a.

Answer 2

thank you!

Answer 3

1. To find the velocity as a function of time, we need to differentiate the position function with respect to time.

Given: s = 24t + 3t^2 - t^3

Taking the derivative of s with respect to t gives us the velocity function:

v = d(s)/dt = d/dt(24t + 3t^2 - t^3)

Differentiating each term separately:

v = 24 + 6t - 3t^2

Therefore, the velocity as a function of time is:
v = 24 + 6t - 3t^2

So, the correct answer is option d: v = 24 + 6t - 3t².

2. To find the velocity of the body at t = 3 seconds, substitute t = 3 into the velocity function we found in the previous step:

v = 24 + 6t - 3t^2
v = 24 + 6(3) - 3(3^2)
v = 24 + 18 - 27
v = 15 m/s

Therefore, the correct answer is option a: 15 m/s.

Answer 4

1. To find the body's velocity as a function of time, we need to take the derivative of the distance function with respect to time. Let's break down the given equation:

s = 24t + 3t^2 - t^3

Taking the derivative of s with respect to t:

v = d(s)/dt = d(24t)/dt + d(3t^2)/dt + d(-t^3)/dt
v = 24 + 6t - 3t^2

So, the velocity of the body as a function of time is v = 24 + 6t - 3t^2.

Now, let's analyze the options:

a. v = 30t - 3t^2 - This is close to the correct answer but missing the initial velocity term, so it is not correct.
b. v = 30t - t^2 - This is incorrect as it is missing the constant term.
c. v = 24 + 3t - t^2 - This is incorrect as it does not have the linear term.
d. v = 24 + 6t - 3t^2 - This is the correct answer as it matches our calculated velocity function.

Therefore, the correct answer is d. v = 24 + 6t - 3t^2.

2. To find the velocity of the body at t = 3 seconds, we can substitute t = 3 into the velocity function:

v = 24 + 6t - 3t^2
v = 24 + 6(3) - 3(3)^2
v = 24 + 18 - 3(9)
v = 24 + 18 - 27
v = 42 - 27
v = 15 m/s

So, the correct answer is a. 15 m/s.