Question

A rocket-driven sled running on a straight, level track has been used to study the physiological effects of large accelerations on astronauts. One such sled can attain a speed of 401 m/s in 1.6 s starting from rest. What is the acceleration of the sled, assuming it is constant? Answer in units of m/s. How far does the sled travel in 1.6 s, starting from rest? Answer in units of m.

Answer 1

a=250.62m/s^2

x=320.8m

Step-by-step explanation:

A body that moves with constant acceleration means that it moves in "a uniformly accelerated motion", which means that if the velocity is plotted with respect to time we will find a line and its slope will be the value of the acceleration, it determines how much it changes the speed with respect to time.

When performing a mathematical demonstration, it is found that the equations that define this movement are as follows.

Vf=Vo+a.t (1)

{Vf^{2}-Vo^2}/{2.a} =X (2)

X=Xo+ VoT+0.5at^{2} (3)

X=(Vf+Vo)T/2 (4)

Where

Vf = final speed

Vo = Initial speed

T = time

A = acceleration

X = displacement

In conclusion to solve any problem related to a body that moves with constant acceleration we use the 4 above equations and use algebra to solve

for this case we use the ecuation number 1

Vf=401m/S

Vo=0m/s

t=1.6s

`Vf=Vo+a.t\\a=(Vf-Vo)/(t) \\\\a=(401-0)/(1.6) =250.62m/s^2`

for the second part we use the ecuation number 2

`\frac{ {Vf^(2)-Vo^2}}{2a} =X\\\frac{ {401^(2)-0^2}}{2(250.625)} =320.8m\\`