Respuesta :
a) The motion described by the particle is undoubtedly a uniformly accelerated rectilinear motion, since the trajectory is rectilinear and the acceleration is constant.
b) In order to calculate the acceleration, we must apply the formula mentioned above, in such a way that the acceleration gives us:
[tex]\boldsymbol{a=\dfrac{v-v_{o}}{t-t_{o} }=\dfrac{25-5}{10-0 }=\dfrac{20}{10}=2 \ m/s^2 }[/tex]
Our acceleration is 2 meters per second squared.
c) We are asked to calculate the function of velocity in relation to time, we simply substitute in the formula.
[tex]\boldsymbol{v=v0+at }\\\boldsymbol{v=2+5t }[/tex]
Very easy!!.
d) To know what speed the particle will have at the instant of t = 8s, it is enough to substitute the value of “t” in the previous formula.
[tex]\boldsymbol{v=5+2(8)=5+16=21 \ m/s }[/tex]
So the speed at time t = 8s is 21 m/s²
e) In this case we are asked to determine at what instant of time the particle will have a speed of 15 m/s, we replace this value in the formula, simply clearing the variable "t", that is:
[tex]\boldsymbol{v=v_{0}+at }[/tex]
Clearing "t"
[tex]\boldsymbol{t=\dfrac{v-v_{o}}{a} }[/tex]
Substituting the speed value
[tex]\boldsymbol{t=\dfrac{v-v_{o}}{a}=\dfrac{15-5}{2}=\dfrac{10}{2}=5 \ seg }[/tex]
That is to say that when the particle has a speed of 15 m/s, it will happen exactly at 5 seconds.
