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