position, velocity, acceleration, & speed of a snowboarder
TRANSCRIPT
Position, Velocity, Acceleration, &
Speed of a Snowboarder
x0 4.49
slope type X trem e halfp ipe
show f'x 0show f''x 0
5 3 2 1 0 .5
0
0 .51
235
y 0
Describe the snowboarder’s motion. y(x) represents the snowboarder’s position.
x0 4.49
slope type X trem e halfp ipe
show f'x 0show f''x 0
5 3 2 1 0 .5
0
0 .51
235
y 0
y’(x) > 0 Velocity of snowboarder is positive. Snowboarder’s position is increasing.
x0 4.49
slope type X trem e halfp ipe
show f'x 0show f''x 0
5 3 2 1 0 .5
0
0 .51
235
y 0
y’’(x) > 0Acceleration of snowboarder is positive.
Snowboarder’s velocity is increasing.
x0 4.49
slope type X trem e halfp ipe
show f'x 0show f''x 0
5 3 2 1 0 .5
0
0 .51
235
y 0
y’(x) > 0 and y’’(x) > 0 Snowboarder is speeding up.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
Describe the snowboarder’s motion. y(x) represents the snowboarder’s position.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
y’(x) > 0 Velocity of snowboarder is positive. Snowboarder’s position is increasing.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
y’’(x) < 0Acceleration of snowboarder is negative.
Snowboarder’s velocity is decreasing.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
y’(x) > 0 and y’’(x) < 0Snowboarder is slowing down.
Describe the snowboarder’s motion. y(x) represents the snowboarder’s position.
y’(x) < 0 Velocity of snowboarder is negative. Snowboarder’s position is decreasing.
y’’(x) > 0Acceleration of snowboarder is positive. Snowboarder’s velocity is increasing.
y’(x) < 0 and y’’(x) > 0Snowboarder is slowing down.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
Describe the snowboarder’s motion. y(x) represents the snowboarder’s position.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
y’(x) < 0 Velocity of snowboarder is negative. Snowboarder’s position is decreasing.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
y’’(x) < 0Acceleration of snowboarder is negative. Snowboarder’s velocity is decreasing.
5 3 2 1 0 .5
0
0 .51
235
y' ' 0
y’(x) < 0 and y’’(x) < 0Snowboarder is speeding up.
Snowboarding over Derivatives at:
demonstrations.wolfram.com/SnowboardingOverDerivatives/