Question

A body moving in the positive x direction passes the origin at time t = 0. Between t = 0 and t = 1 second, the body has a constant speed of 24 meters per second. At t = 1 second, the body is given a constant acceleration of 6 meters per second squared in the negative x direction. The position x of the body at t = 11 seconds is

-99? I think I did this wrong

Answer 1

at t = 1 it is at x = 24
a = -6
so now start over for 10 seconds to get to t = 11
at new time = 0, Vi = +24 and a = -6
v = 24 - 6 t
x = 24 + 24 t - (1/2)6 t^2
at t = 10
x = 24*10 - 3 (100)
240 - 300 is indeed not -99

Answer 2

ok now I'm even more confused. So the answer is -60?
But the options for the question are
a)- 99 m
b)+ 99 m
c)+ 36 m
d)- 75 m
e)- 36 m

Answer 3

so I tried plugging 11 into that x= 24 + 24t - (1/2) t^2 and I got -75. Would that be the right answer?

Answer 4

I suspect that the problem writer used 11 instead of 10 seconds for the second part, but that is wrong. Choose -75

Answer 5

Answer: Because your acceleration from t=1 to t=11 is 6 meters per second squared. All you need to do is integrate 6 to get the velocity. You would get 6x+c. Ignoring the constant, just multiply 6 by 10 seconds. 6(10) = 60, you get that for a body with a constant acceleration of 6 meters per second squared, in 10 seconds, it will travel a total of 60 meters. However, since this is in the negative-x direction, you must subtract this from the 24 meters in which the body already traveled in the 1st second. 24-60, you will get -36m.