Aparticle's velocity is described by the function vx = t 2 - 7t + 10 m/s, where t is in s. a. at what times does the particle reach its turning points? b. what is the particle's acceleration at each of the turning points?

The turning point of the particle is at 3.5 seconds with an acceleration of 0.

Acceleration is the time rate of change of velocity. It is given by the equation:

Acceleration = change in velocity / change in time

Given the velocity equation:

v = t² - 7t + 10

The turning point is at dv/dt = 0, hence:

dv/dt = 2t - 7

2t - 7 = 0

t = 3.5 seconds

Acceleration (a) = dv/dt

a = 2t - 7

a(3.5) = 2(3.5) - 7 = 0

The turning point of the particle is at 3.5 seconds with an acceleration of 0.

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velocity is given as

when the object reached to its turning its velocity will be zero

so it will reach its turning at two time instant

Part b)

For acceleration we know that

now at t = 2

also at t=5

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.